Name:
Date:
Why we are doing this. This check-in helps us see what you already know and which math ideas we should practice more, so we can plan lessons that give you the instruction you need.
- This is not a pass-or-fail test, and there are no grades. Just do your best.
- Please do not use a calculator. Show your work in any way you can — writing, pictures, or number lines.
- If you need help reading or hearing the directions, a mentor can help you understand them — but not give you answers.
- Each part has a yellow Strategy box. Try the part first; read the box only if you get stuck. It gives you a first step, never the answer.
WARM-UP
The Order of Operations (PEMDAS)
Look at the letters in the acronym PEMDAS. Write the math word that each letter stands for (for example: "Add" or "Multiply").
1.P
2.E
3.M
4.D
5.A
6.S
Strategy — Say the acronym out loud, one letter at a time, and ask "what math action starts with that sound?" Fill in the letters you are sure of first, then come back to the ones that are left.
PART 1
Is it an Expression or an Equation?
Look for an equals sign (=). If it has one, it is an Equation. If it does not, it is an Expression. For the last two, write the math you hear.
1.2 + 3 (circle one): Expression | Equation
2.4 = 9 (circle one): Expression | Equation
3.7 - 5 = 2 (circle one): Expression | Equation
4.8 - 1 (circle one): Expression | Equation
5.10 = 5 + 5 (circle one): Expression | Equation
6.6 + 4 (circle one): Expression | Equation
7.5 × 2 = 10 (circle one): Expression | Equation
8.9 ÷ 3 (circle one): Expression | Equation
9."Six plus four equals ten." Write it as math:
10."Ten minus five." Write it as math:
Strategy — Before you decide, scan the line for an equals sign and circle it if you find one. That one symbol is the whole test — let it choose your answer.
PART 2
Using Numbers for Real Life
If you have money, write the number. If you owe money, put a minus sign in front. For temperature, you can draw or use a number line if you like.
1.You have $7.
2.You owe $5.
3.Your bank had $10. You spent $6. How much now?
4.It is 3 degrees below zero.
5.It is 5 degrees above zero.
6.You find $4.
7.Which is bigger: -2 or 1? (Use a number line if you want.)
8.Which is smaller: 3 or -5?
9.Maria owes $2 and then gets $5. What does she have now?
10.It was -4 degrees. Then it warmed up by 6 degrees. What is the new temperature?
Strategy — Decide the direction before the size: does the situation add to what you have (a plus) or take away (a minus)? Choose the sign first, then work with the number.
PART 3
Number Line Problems
Draw a number line if it helps. Show your thinking with marks or arrows.
1.Draw a number line and put -3, 0, and 4 on it.
2.Start at -2. Move 5 spaces right. Where do you land?
3.Put in order from smallest to biggest: -1, 2, -4.
4.Start at 6. Move 8 spaces left. Where do you land?
5.Draw zero. What is on the left and right of zero?
6.3 + 7. Use a number line if you want.
7.5 - 9. Use a number line if you want.
8.How far is it from -4 to 2 on a number line?
9.The temperature went from -3 to 4. How much did it change?
10.You start at 0 and lose 6 points. Where are you?
Strategy — Put zero in the middle first, then step one mark at a time: move right for more/warmer, left for less/colder. Count the jumps you make instead of guessing.
PART 4
Doing Steps in the Right Order
For each problem, find what to do first, second, and last. You can number your steps "1," "2," "3," or talk about them. Circle what you do first.
1.2 + 3 × 4
2.(5 + 2) × 3
3.4 × (2 + 3)
4.8 ÷ 2 + 5
5.6 + 2 × 3
6.(10 - 4) + 2
7.5 × 3 + 1
8.2² + 4
9.7 + (5 × 2)
10.Why do you think we have to do math steps in a special order?
Strategy — Look for grouping symbols (parentheses) and any multiply or divide before you touch an add or subtract. Circle the very first operation before you compute anything.
PART 5
Working With Letters (Variables)
Circle the letter — it is called a variable. If the question gives a number for the letter, use it to solve.
1.What is the variable in: x + 2 = 5?
2.Which number never changes in: x + 2 = 5?
3.If x = 4, what is x + 3?
4.If y = 2, what is 2y + 1?
5.Write a math problem with "n" for the number of apples.
6.Which sign means "sum" or "add"?
7.If a = 7, what is a - 3?
8.If b = 5, what is 3b + 2?
9.Write with math: "twice a number n, plus one."
10.A student has x shirts, then gets 2 more. Write the math.
Strategy — The variable is the letter that can change; the constant is the plain number that stays put. When a value is given for the letter, swap it in wherever you see the letter, then do the arithmetic.
💡 Remember
- You can write, draw, use number lines, or talk through your steps — whatever helps you show your thinking.
- You can always ask your mentor for help reading or understanding the directions.
- This is just to help you and your teacher see what to practice for future math learning. Thank you for trying your best!
FOR MENTOR USE — READ BEFORE YOU BEGIN
Mentor Guide
How to run this diagnostic so it stays low-pressure and gives you useful information
1. What this check-in builds
It is a starting picture, not a score. Across six short sections — order of operations, expressions vs. equations, signed numbers in real life, the number line, step order, and variables — it shows which foundations are already solid and which need practice before College Algebra. Treat the result as a map for planning, never a grade.
2. Run it low-pressure
- Say up front: "This is not a test and there are no grades — it just shows us what to practice." Repeat it if the student tenses up.
- No calculator. Encourage writing, drawing, number lines, or thinking out loud — any way of showing work counts.
- Let the student skip and return. A blank answer is data too; it tells you where to start, not that they failed.
3. Using the Strategy nudges
Each part has a yellow Strategy box. Have the student try the part first, and read the box only if they stall. The nudges name a first step or method — "circle the equals sign," "put zero in the middle," "swap the number in for the letter" — and never give the answer or which option is right. If you help read a box aloud, read it as written; do not add the solution.
4. Supporting the student
- Help with reading or hearing the directions when asked — but do not supply answers or confirm whether one is correct.
- Accept an oral answer first, then have them write or draw it — speaking removes the blank-page freeze.
- Watch how they work, not just what they write. Whether they reach for a number line, count on fingers, or guess tells you as much as the final number.
5. Using results to plan lessons
- Look for patterns by section, not single misses: shaky signed numbers or step order point to the next unit to teach.
- Note any item they solved with a number line but not without — that shows a tool they can lean on while a skill develops.
- Turn gaps into a short practice plan, and re-check those specific ideas later to make progress visible to the student.